Answer:
(−∞, 0) ∪ (0, ∞)
Step-by-step explanation:
Given :
u(x) = -2x²
[tex]V(x)=\sqrt{\frac{1}{x} }[/tex]
Determining UoV(x) :
[tex]UoV(x)=U(V(x))=-2\left( \sqrt{\frac{1}{x} } \right)^{2}[/tex]
Then
[tex]UoV(x)=U(V(x))=-2 \times \frac{1}{x}[/tex]
Then
[tex]UoV(x)=U(V(x))=- \frac{2}{x}[/tex]
Since the range of -2/x is all real numbers except zero
Then
The range of UoV is :
(−∞, 0) ∪ (0, ∞)
